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Fiber Bundles and Intersectional Feminism 1 FIBER BUNDLES AND INTERSECTIONAL FEMINISM DAGAN KARP Abstract. This note provides an introduction to, and call for ac- tion for, intersectional feminism for mathematicians. It also serves as an example of mathematical models of social structures, provid- ing an application of geometry to social theory. 1. Gender Inequity in Mathematics Gender inequity is historically severe and remains extant in math- ematics. Although nearly half of all bachelor's1 degrees2 in the U.S. in mathematics are awarded to women according to the Conference Board of the Mathematical Sciences (CBMS) [4], only about 30% of the PhD's in mathematics in the U.S. are awarded to women, and fur- ther only 14% of tenured mathematics faculty are women, according to the American Mathematical Society (AMS) Annual Survey [19]. See Section 2 for a discussion of gender and gendered terms. The underrepresentation of women in mathematics is persistent and pervasive. Comparing previous CMBS and AMS Annual Survey Data3, we see that these critical transition points are persistent. For example, the percentage of women PhD recipients in mathematics has remained at roughly 30% for at least two decades. Hence, there is persistent gender inequity at the level of participation and representation. It is worth noting that such underrepresentation extends throughout the profession. For example, \women are underrepresented as authors of mathematics papers on the arχiv, even in comparison to the proportion of women who hold full-time positions in mathematics departments"[7]. Such patters continue to appear in peer-reviewed publications [32]. Women are also underrepresented in journal editorial boards in the mathematical sciences [39]. Gender inequity in mathematics extends well beyond representation { beyond counting bodies in the profession. The non-academic obstruc- tions to success in mathematics for women are myriad. These include not only lack of role models and senior mentors as above, but also individual bias and structural inequities within and across institutions. Date: February 24, 2020. 1An unmarried man, according to Merriam-Webster, whereas a maid is therein defined as an unmarried girl or woman, especially when young or a virgin. 2Note the persistent misogyny in the use of B.S. and B.A. degrees. Why not all maid's degrees? 3AMS data is archived and updated at http://www.ams.org/profession/data/ annual-survey/annual-survey 1 Individual bias (inherent, implicit, intentional, or otherwise) is one cause of gender inequity in mathematics. Moss-Racusin et al performed a seminal study demonstrating such bias in the sciences. In a randomized double-blind study (n = 127), science faculty from research-intensive universities rated the ap- plication materials of a student { who was randomly assigned either a male or female name { for a laboratory manager position. Faculty participants rated the male applicant as significantly more competent and hireable than the (identical) female applicant.[35] Similarly, in another major study, over 6,500 faculty from 89 insti- tutions were sent emails from fictitious students inquiring about re- search opportunities prior to applying to a doctoral program. These emails were identical in all but the name of the students; names were randomly assigned to signal gender and race. The study found \fac- ulty were significantly more responsive to Caucasian males than to all other categories of students, collectively, particularly in higher-paying disciplines and private institutions" [33]. Harvard's Project Implicit4 has generated thousands of citations demonstrating implicit bias along axes of gender identity (among others). For example, in one publi- cation, Zitelny et al find that \Implicit measures of the gender-science stereotype are often better than explicit measures in predicting relevant outcomes"[41]. Much more important than bias held by individuals, there are sys- temic obstructions to success for women in mathematics. Although actions are taken by individuals, when they coalesce into clearly de- fined patters, it is necessary to recognize bias in the underlying in- stitution or system in place. For example, beginning in kindergarten and increasing with age, \Teachers consistently rate girls mathemati- cal proficiency lower than that of boys with similar achievement and learning behaviors" [10]. The evidence suggests that the U.S. educa- tion system is biased against women and privileges men from the very beginning of school. This is much more dangerous than individual bias. For an important, sophisticated, and nuanced critique of the emphasis on individual implicit bias and diversity, see [36]. In addition to a system of education biased against women, women face countless other obstructions to success in mathematics. These include, but are not limited to, macroaggressions, microaggressions, cultural exclusion, lack of role models, lack of peer support, and sexual harassment. An (problematized) attempt was made to describe some of the landscape of obstructions to equitable participation in mathematics conferences here [31]. It is imperative to listen to women and those targeted by heteronormative misogyny themselves, as Izabella Laba persuasively points out [28]. I suggest looking to the blogs of Laba5, 4https://implicit.harvard.edu/implicit/ 5https://ilaba.wordpress.com/ 2 Piper H.6, Chanda Prescod-Weinstein7 and the Inclusion/Exclusion8 blog of the AMS. A word on essentialism and reduction. I have neither the lived ex- perience nor professional training to exhaustively analyze systemic and institutional misogyny in mathematics. Rather, here I am only try- ing to give a glimpse of biased systems, as motivation for engaging in feminist work. Of course it would be ridiculous and essentializing to assume that any single individual, woman or otherwise, could speak on behalf of All Women, cis and trans, regardless of income, race, ethnic- ity, country of origin, first language, and all other aspects of identity. As Audre Lorde points out, \It is a particular academic arrogance to assume any discussion of feminist theory without examining our many differences, and without a significant input from poor women, Black and Third World women, and lesbians"[29]. Also, as women are nei- ther the architects nor the beneficiaries of misogyny, it is necessary for all people, but especially men and those who are privileged by misog- yny, to engage in the lifelong process of critical self-examination and the urgent work to dismantle systems of gender bias. 2. Language The moduli space of genders is neither connected nor equidimen- sional. It is certainly not the disjoint union of two points. It is also certainly not linear with a canonical well ordering. It is not even fixed in time. So the gender binary is an incorrect model mathematically, as is a linear gender spectrum. There is instead a rich moduli space of gender identities determined by self-identification, including people who are nonbinary, agender individuals, and people with genders that are multiple or change as a function of time. The word woman hence of course must be used to refer to an individual who self-identifies as such at a given point it time. However historical surveys of the mathemat- ical sciences not only assume the false gender binary, but also assign gender based on presentation. As such, there is an insufficiently an- alyzed disconnect between historical and current language and survey data. For an introduction to gender studies, including importantly the performative nature of gender, I refer the reader to the canonical text by Butler [8]. I am also intentional in my use of the phrase intersectional feminism. Because mathematicians use existential and universal quantifiers pro- fessionally, there is an unfortunate tendency by some in the field to propose an All Lives Matter approach to issues of equity in mathemat- ics. I use intersectional feminism, as opposed to intersectionality, to highlight intersectionality as a feminist movement and framework and to highlight the brilliance and work of women, especially queer women 6http://www.theliberatedmathematician.com/blog/ 7https://medium.com/@chanda 8https://blogs.ams.org/inclusionexclusion/ 3 of color, who have lead this struggle for social justice and continue to do so in greater society and also in mathematics. 3. Feminism In the Feminism and Visual Culture Reader, Amelia Jones writes Feminism is, of course, not a singular discourse to be easily defined or pinned down. Although its emergences (from the burgeoning of the suffragette movements in the late nineteenth and early twentieth centuries to the rise of women's lib in the 1960s and beyond) can be loosely mapped, its parameters and positions are under contin- ual negotiation. This book takes feminism seriously but does not seek to patrol its boarders by, for example, la- beling authors [...] 'feminist' or 'not feminist.' This kind of strategy is antithetical to the best impulses of what I take to be feminism. [25] To give a comprehensive introduction and history of feminism is not only beyond the scope of this article, and my capabilities, but in ad- dition I am not interested in pursuing a definitive treatment for the reasons Jones expresses above. Rather, I'll provide here a very terse in- troduction, intended for mathematicians who consider themselves gen- erally unaware of the subject. There is a universe of scholarship sur- rounding feminist history and thought. To recommend just three texts, I suggest [1], [2], and [37]. Feminism may (reductively) be described in terms of waves of the movement. First wave feminism, from the mid-nineteenth to the early twentieth century, was centrally concerned with women's legal and po- litical rights, such as the basic rights to vote, own property, control property, and earn and control their own income (i.e. have separate economy). The first wave of feminism roughly ends with the ratifica- tion of the 19th Amendment in 1920. Key figures include Elizabeth Cady Stanton and Sojourner Truth. Second wave feminism dates roughly from the 1960s through the 1980s. Second wave feminism moved the fight from equality under the law to social equality.
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